Yes I am leaving out a bunch of steps because ultimately what happens in the problem is that the expression 3x^(2)-1 is moved into the denominator as per the rule for taking the derivative of natural log of x.

I don't understand why the derivative of the natural love of 3x would equal 1/x but the derivative of 3x^(2)-1 is 1/3x^(2)-1

You might want to verify the actual derivative. The result displayed at your link does not match what you've posted.

To learn the "why", clearly write out each stage of the computation in each derivative. If you are unable to match the correct expressions, kindly please reply showing your work, so that errors may be located and explicated. Thank you.